The amount remaining of a certain radioactive substance after t days is A(t)=A0e^-0.025t , where A0 is the beginning amount. how much do we need to begin with if we want 75 grams after 15 days? round your answer to one decimal place.

Q: The half-life of Erbium-171 is 7.5 hours. What is the hourly decay rate? Express the result to four…

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Q: The radioactive isotope of lead Pb-209, decays at a rate proportional to the amount present at any…

A: The differential equation for decay is dAdt=kA dAA=k·dt ⇒∫dAA=∫k·dt⇒lnA=kt+c1A=ekt+c1A=ektec1A=Cekt…

Q: A cell culture contains 7 thousand cells, and is 0.12t thousand cells growing at a rate of r(t) per…

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Q: A radioactive substance decreases from 10 grams to 9 grams in 9.4 hours. Find its half-life. Express…

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Q: A certain radioactive element decomposses at a rate proportional to the amount present. If 100…

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Q: The half-life of Radium-226 is 1590 years. If a sample contains 300 mg, how many mg will remain…

A: Half life = 1590 years Inititial amount of sample (a0) = 300 mg Final amount of sample (af) = ?

Q: Yttirum-90 has a half-life of 64.10 hours. Given an initial mass of 622 grams of the sample, how…

A: Given information Half life t12=64.10 hours And the initial mass m0=622 grams We have to find the…

Q: Yttirum-90 has a half-life of 64.10 hours. Given an initial mass of 659 grams of the sample, how…

A: Half-life is the time required for a quantity to reduce to half of its initial value. The term is…

Q: Find the missing values assuming continuously compounded interest. (Round your answers to two…

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Q: Heather wants to invest $35,000 of her retirement. She can invest at 4.8% simple interest for 20 yr,…

A: Simple interest is applied only on the principal amount every year. The interest amount accumulated…

Q: The half-life of carbon-14 is 5730 years. How long does it take for 3.4 grams of carbon-14 to be…

A: We have to find

Q: The half-life of Radium-226 is 1590 years. If a sample contains 200 mg, how many mg will remain…

A:

Q: A quantity with an initial value of 220 grows continuously at a rate of 9.5% per hour. What is the…

A: Consider the provided question, Given, initial value = 220  Rate, r = 9.5% = 0.095 per hour t = 225…

Q: Suppose the population of a city has been growing at a rate of 2.5% per year for each of the last 8…

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Q: A radioactive element has a half-life of 136 yea What is its continuous rate of decay? Number %…

A: Decay constant =ln 2t12t12 =136 yearsDecay constant =ln 2136                            =0.51%

Q: The half-life of radioactive cobalt is 5.27 years. Suppose that a nuclear accident has left the…

A: Given:    Half-life of radioactive cobalt =5.27 years    The proportion p that remains after y years…

Q: Radon-222 has a half-life of 4.00 days. Given its mass 5.937 gram at a certain time, what was the…

A: We will find out the required value.

Q: Radioactive cesium-137 has a half-life of 30.17 years. How much of an initial amount of 1,000…

A: If N0 is the initial amount and t is the number of years then equation of decay  is given by…

Q: Of an initial amount of 5000 g of lead-210, how much will remain in 120 years? Lead-210 decays at a…

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Q: Of an initial amount of 9000 g of lead-210, how much will remain in 120 years? Lead-210 decays at a…

A: Apply the formula  P(t)=Po(1-r)t where, Po is the initial quantity r is the rate and t is the time.…

Q: A wolf population is growing at a rate of 9.3% per year. Find the time at which the wolf population…

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Q: derive a formula for the of time that takes money to increase by one and half in a bank account that…

A: We have R= 3% compounded  yearly Let say it will take t years

Q: Yttirum-90 has a half-life of 64.10 hours. Given an initial mass of 551 grams of the sample, how…

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Q: Radioactive radium has a half-life of 1899 years. If 20g of the substance are present initially,…

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Q: The drug Valium is eliminated from the bloodstream exponentially with a half-fe of 36 hours. Suppose…

A: Given - The drug Valium is estimated from the bloodstream exponentially with a half-life of 36…

Q: Radon-222 has a half-life of 4.00 days. Given its mass 3.055 gram at a certain time, what was the…

A:

Q: The half-life of carbon-14 is 5730 years. How long does it take for 3.9 grams of carbon-14 to be…

A: h=5730 years. x=final amount=1.7 grams. y=initial amount=3.9 grams. t=h(ln(x/y))/ln(1/2)…

Q: The half-life of radium-225 is approximately 14.9 days. How much of a 15 gram sample of radium-225…

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Q: A government agency estimates the number of young adults (ages 18 to 24) in a particular country to…

A: Given that       A Government agency estimates the number of young adults (ages 18 to 24) in a…

Q: The rate of active element carbon 14 has a 1/2 life of 5750 years a scientist determined that the…

A: Given: carbon 14 has a 1/2 life of 5750 years  To find : how old were the bones at the time they…

Q: A radioactive substance used in nuclear weapons decays at the rate of 3.2% per year. Calculate the…

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Q: A tumor is injected with 0.4 grams of Iodine-125, which has a decay rate of 1.15% per day. To the…

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Q: A tumor is injected with 0.9 grams of Iodine-125, which has a decay rate of 1.15% per day. To the…

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Q: 2. Suppose that a bacteria population is dying off at a rate of 30% per day. How much of the…

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Q: Suppose the amount of a certain radioactive substance in a sample decays from 3.60 mg to 800. pg…

A: We have to find the half life of substance.

Q: Find the missing values assuming continuously compounded interest. (Round your answers to two…

A:

Q: A certain radioactive substance decomposes at a rate proportional to the amount present. Of the 1000…

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Q: The half-life of a radioactive substance is 160 years. a) Compute the decay constant k (4 decimal…

A: a)Half-Life of a radioactive substance is 160 years, Initial amount=300 g time, t=160 years,We know…

Q: A radioactive material decays at a rate proportional to its amount. If the material has a half-life…

A: model is  A=A0ektfor half-life put A=A02thenA02=A0ektsolving for t, we get k=-ln(2)t

Q: A quantity with an initial value of 870 decays continously at a rate of 0.75% per day. What is the…

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Q: A certain radioactive material is known to decay at a rate proportional to the amount present.…

A: Given a certain radioactive material is known to decay at a rate proportional to the amount present.…

Q: The drug Valium is eliminated from the bloodstream exponentially with a half-life of 36 hours.…

A: Given that the initial dose is 40 milligrams of valium at midnight. The half-life of valium is 36…

Q: A wooden artifact from an ancient tomb contains 65% of the carbon-14 that is present in living…

A: the radioactive decay equation is  given by m=m0e-ln2t't where t' is the half life. the tomb…

Q: how long will it take $800 to triple if it is invested at an annual intrest rate of 5.3%

A: P=$800 , R=5.3%

Q: It has been estimated that the world's tropical rain forests are disappearing at the rate of 1.8%…

A: To Determine:  how soon will the rain forests be reduced to 25% of their present size? Given: It has…

Q: The half-life of carbon-14 is 5730 years. How long does it take for 2.1 grams of carbon-14 to be…

A: A(t)=A0(1/2)t/h h is the half life A0 is the initial value

Q: Find the interest rate needed for an investment of $3,000 to grow to an amount of $4,000 in 4 yr if…

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Q: he radioactive isotope gallium 67 has a biological half-life of 36 hours. If re start with 100…

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Q: Yttirum-90 has a half-life of 64.10 hours. Given an initial mass of 750 grams of the sample, how…

A: See the detailed solution below.

Q: The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time…

A: Given- Half life t12 =3.3 hours, Intial weight=1 gm. To find- The time in which the radioactive…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.